There are known convertible vehicles, which have two consecutive roof elements in the closed condition, one of which, the rear element, can swivel downwards about a transverse axis in relation to the car body, so that in the stowed-away condition it lies essentially horizontal and with its side facing the passenger compartment pointing upward when the roof is closed. The front roof element when opening the roof can swivel onto the rear roof element about a second transverse axis situated in the boundary region between the roof elements and in the opened state it is oriented in opposite sense to the former. In order to relay the opening and closing motion also to the front roof element, there are provided two rod elements on each side of the vehicle, extending from a main bearing in the car body and as far as the connection region of the rear and front roof elements, which open and close in the manner of a parallelogram when the roof is moved. The rod elements are often also known as guide rods and main guide rods. Due to their mutual opening and closing, these elements disturb the visual field during the opening process and there is a danger of getting caught between the rods as they close. Furthermore, a considerable expense must be incurred for paneling in the rear roof element to prevent at least the front rod of the two from being visible when the roof is closed.